The Spearman correlation Aa Aa The rapid growth of video game popularity has generated concern among practitioners, parents, scholars, and politicians," wrote researchers Hope M

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The Spearman correlation Aa Aa

The rapid growth of video game popularity has generated concern among practitioners, parents, scholars, and politicians," wrote researchers Hope M. Cummings and Elizabeth A. Vandewater. In their study, Cummings and Vandewater measured the time adolescents spent playing video games as well as time spent doing other activities, such as interacting with family and friends, reading or doing homework, or playing sports. [Source: Cummings, H., & Vandewater, E. (2007). Relation of adolescent video game play to time spent in other activities. Archives of Pediatrics & Adolescent Medicine, 161(7), 684-689.]

After reading about the study conducted by Cummings and Vandewater,  you decide to conduct a similar study among a sample of 9 teenage boys. You ask the boys to keep a log of their activities for a day. You want to test whether the amount of time boys spend playing video games is correlated with the amount of time they play with a sibling or peer. You realize that because some of the boys in your sample do not play video games at all, your data will have many zeroes for the amount of time they play video games

You decide to use the Spearman correlation for the data. The first thing you do is convert the data to ranks. You convert the amount of time each boy plays video games by assigning the lowest rank to the five boys who don' play video games and the highest rank to those who play video games the most. The rank you assign to each of the five boys who don't play video games is

The following table consists of the data for the 9 boys in your study. The data are sorted in order of the amount of time the boys spent playing video games. Fill in the missing ranks for the time spent playing video games and the ranks for the time spent playing with a sibling or peer. Note that the time spent playing with a sibling or peer is not sorted in order.

Time spent  Playing Video Game (Minutes/Day)

0 

0

0

0

0

20

33

82

126

Time spent Playing with a Sibling or Peer(Minutes/Day) 

60

162

221

130

215

200

130

65

85

Rank of  Time Spent Playing Video Games

your answer above)

your answer above)

your answer above)

your answer above)

your answer above)

Rank of  Time spent with a sibling or  Peer

1

Using your completed table, you can calculate the Spearman correlation in two different ways. One way is to use the Pearson correlation formula on the ranks of the data. When you do this, you get rs = -0.42. The second way to calculate the Spearman correlation is to use the following formula:

1-6sigmaD2/  n(n^2 - 1)

In this formula, D represents the difference between ranks for each individual. Using this formula, you get r = -0.30. These two estimates of the Spearman correlation are different for the following reason:

The Pearson correlation formula applied to the ranks loses accuracy when there are many ties.

The formula that uses the differences (D) loses accuracy when there are many ties.

The formula that uses the differences (D) is always only a rough estimate of rs.

You do not use the Pearson correlation formula when calculating the Spearman correlation.